
Serrin [1]}, Struwe [2]}, Escauriaza, Seregin and Šverák [3]}
\(u\in L^{p} (0,T;L^{q}( \mathbb {R}^{3})) ~~~ \text{with}~~~~2/p+3/q=1, ~~q\ge 3.\) 

Beirao da Veiga [4]}
\(\nabla u\in L^{p} (0,T;L^{q}( \mathbb {R}^{3})) ~~~ \text{with}~~~~2/p+3/q=2 , ~~q>3/2.\) 

Berselli and Galdi [5]}, Zhou [6]}, [7]}
\(\Pi \in L^{p} (0,T;L^{q}( \mathbb {R}^{3})) ~~~ \text{with}~~~~2/p+3/q=2 , ~~q>3/2.\) 

